In a 200 m race, A runs at a speed of 2 m/s. If A gives B a start of 10 m and still beats him by 5 s, what will be the Speed of B?

Options

A. `1 (17)/(21)` m/s
B. `3 (17)/(21)`m/s
C. `21 m//s`
D. `2 m//s`

Answer

To solve the problem step by step, we will analyze the given information and calculate the speed of B.

### Step 1: Identify the given data
- A's speed = 2 m/s
- Distance of the race = 200 m
- B's start = 10 m (which means B runs 190 m in the race)
- A beats B by 5 seconds

### Step 2: Calculate the time taken by A to finish the race
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

For A:
\[ \text{Time taken by A} = \frac{200 \text{ m}}{2 \text{ m/s}} = 100 \text{ seconds} \]

### Step 3: Calculate the time taken by B to finish the race
Since A beats B by 5 seconds, the time taken by B is:
\[ \text{Time taken by B} = \text{Time taken by A} + 5 \text{ seconds} \]
\[ \text{Time taken by B} = 100 \text{ seconds} + 5 \text{ seconds} = 105 \text{ seconds} \]

### Step 4: Calculate the distance covered by B
B runs 190 m in the race (because A gives B a start of 10 m):
- Distance covered by B = 190 m

### Step 5: Calculate the speed of B
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For B:
\[ \text{Speed of B} = \frac{190 \text{ m}}{105 \text{ seconds}} \]

### Step 6: Simplify the speed of B
To simplify:
\[ \text{Speed of B} = \frac{190}{105} \]

We can simplify this fraction:
- Divide both the numerator and denominator by 5:
\[ \text{Speed of B} = \frac{38}{21} \text{ m/s} \]

### Step 7: Convert to mixed fraction (if necessary)
To convert \( \frac{38}{21} \) to a mixed number:
- 21 goes into 38 one time (1), with a remainder of 17.
- Thus, \( \frac{38}{21} = 1 \frac{17}{21} \text{ m/s} \)

### Final Answer
The speed of B is \( \frac{38}{21} \) m/s or approximately 1.62 m/s.